# Math 114 Course Descriptions

The topic for **Math 114 Section 02A for Fall 2020** is "The mathematics of the visual arts." The class will cover some topics of mathematics that may be related with the visual arts and we will probably covering of parts of mathematics that you may have not that is used is other topics that you may not realize that mathematics is used in that area.

The topic for **Math 114 Section 01J for Fall 2020** is "The mathematics of politics." We will look at questions such as the following.

In an election with more than two candidates, what is the "most just" way to determine a winner if no candidate wins more than 50% of the votes? Should we simply select the candidate with the most votes? Or should we take into account voters' rankings of the candidates (each voter's 2nd choice, 3rd choice, etc.) -- and if so, how? And how do we assess the fairness of a particular method?

If a legislative body is to have "proportional representation", and the number of seats is fixed by law, how do we handle the round-offs we get when we determine what fraction of the seats a particular state is supposed to receive? For the U.S. House, various methods have been proposed by Alexander Hamilton, Thomas Jefferson and others until a method was settled upon in the mid-twentieth century. We will see that there are hidden political "traps" inherent in seemingly innocent mathematical calculations.

In a body with "voting blocs", how much power does a particular bloc really have? The actual number of votes can be a misleading measure.

Is the Electoral College "fair?" What do we even mean by "fair?"

For most of the course you will not need to use anything more high-powered than arithmetic, although there are some topics that will involve some algebra. On the other hand, high school geometry actually is quite relevant to this course, in the following sense. I will expect you to construct logical arguments, just as you were expected to prove geometric theorems. But rather than being asked to prove that triangles have a particular property, you will be asked to argue that a particular voting method satisfies a certain fairness criterion, for example. We will actually encounter some theorems that people have proven which paint a pessimistic picture of "how fair" a voting method or an apportionment method can be.

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## Recent Topics:

The topic for **Math 114 for Spring 2020** is "The mathematics of the visual arts." The class will cover some topics of mathematics that may be related with the visual arts and we will probably covering of parts of mathematics that you may have not that is used is other topics that you may not realize that mathematics is used in that area.

The topic for **Math 114 for Fall 2019** is "The mathematics of politics." We will look at questions such as the following.

In an election with more than two candidates, what is the "most just" way to determine a winner if no candidate wins more than 50% of the votes? Should we simply select the candidate with the most votes? Or should we take into account voters' rankings of the candidates (each voter's 2nd choice, 3rd choice, etc.) -- and if so, how? And how do we assess the fairness of a particular method?

If a legislative body is to have "proportional representation", and the number of seats is fixed by law, how do we handle the round-offs we get when we determine what fraction of the seats a particular state is supposed to receive? For the U.S. House, various methods have been proposed by Alexander Hamilton, Thomas Jefferson and others until a method was settled upon in the mid-twentieth century. We will see that there are hidden political "traps" inherent in seemingly innocent mathematical calculations.

In a body with "voting blocs", how much power does a particular bloc really have? The actual number of votes can be a misleading measure.

Is the Electoral College "fair?" What do we even mean by "fair?"

For most of the course you will not need to use anything more high-powered than arithmetic, although there are some topics that will involve some algebra. On the other hand, high school geometry actually is quite relevant to this course, in the following sense. I will expect you to construct logical arguments, just as you were expected to prove geometric theorems. But rather than being asked to prove that triangles have a particular property, you will be asked to argue that a particular voting method satisfies a certain fairness criterion, for example. We will actually encounter some theorems that people have proven which paint a pessimistic picture of "how fair" a voting method or an apportionment method can be.